Papers › Fast estimation of outcome probabilities for quantum circuits
Fast estimation of outcome probabilities for quantum circuits
Hakop Pashayan, Oliver Reardon-Smith, Kamil Korzekwa, Stephen D. Bartlett
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We present two classical algorithms for the simulation of universal quantum circuits on n qubits constructed from c instances of Clifford gates and t arbitrary-angle Z-rotation gates such as T gates. Our algorithms complement each other by performing best in different parameter regimes. The Estimate algorithm produces an additive precision estimate of the Born rule probability of a chosen measurement outcome with the only source of run-time inefficiency being a linear dependence on the stabilizer extent (which scales like ≈1.17ᵗ for T gates). Our algorithm is state-of-the-art for this task: as an example, in approximately 13 hours (on a standard desktop computer), we estimated the Born rule probability to within an additive error of 0.03, for a 50-qubit, 60 non-Clifford gate quantum circuit with more than 2000 Clifford gates. Our second algorithm, Compute, calculates the probability of a chosen measurement outcome to machine precision with run-time O(2ᵗ⁻ʳ t) where r is an efficiently computable, circuit-specific quantity. With high probability, r is very close to min{t, n-w} for random circuits with many Clifford gates, where w is the number of measured qubits. Compute can be effective in surprisingly challenging parameter regimes, e.g., we can randomly sample Clifford+T circuits with n=55, w=5, c=10⁵ and t=80 T gates, and then compute the Born rule probability with a run-time consistently less than 10 minutes using a single core of a standard desktop computer. We provide a C+Python implementation of our algorithms and benchmark them using random circuits, the hidden shift algorithm and the quantum approximate optimization algorithm (QAOA).
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